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# Def/Inverse function

Definition of Inverse function: Suppose that $X$ and $Y$ are sets, and $f \colon X \rightarrow Y$ is a function. Suppose that $g \colon Y \rightarrow X$ is another function. There are three notions of "inverse function", defined as follows:

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Function, Def/Identity function

The following statements and definitions logically rely on the material of this page: State/Injective functions have left inverses, and State/Surjective functions have right inverses

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Functions